 Hello and welcome to the session. In this session we will discuss a question which says that find the equations of the tangents to the circle, x square plus y square is equal to 25, drawn from the point to 5. Now before starting the solution of this question, we should know a result. And that is the equations of the tangents in the circle, x square plus y square is equal to a square are given by y is equal to nx plus minus a into square root of 1 plus n square where this is slope of the tangent and a is the radius of the circle. Now this result will work out as a key idea for solving out this question. And now, we will start with the solution. Now here the equation of the circle is given to us. So given the equation of the circle is x square plus y square is equal to 25. This implies x square plus y square is equal to 5 square, so where the radius is equal to 5. Now using the result which is given in the key idea, the radius here and radius is always positive. So we have any tangent to the given circle plus y square is equal to 25 is y is equal to mx plus 5 into root 1 plus m square. It is also given that the tangent is drawn from the point to 5. Given point y is equal to 5 and x is equal to 2 here we have into m plus 5 into root 1 plus m square. It implies 5 minus 2n is equal to 5 into root 1 plus n square. Now square both sides this implies 5 minus 2n whole square is equal to 5 into root 1 plus m square which further implies plus 4n square minus 20m is equal to 25 into 1 plus m square per whole. Which implies minus 20m is equal to 25 plus 25m square. This implies 25 plus 4m square minus 20m minus 25 minus 25m square. Now these terms are pencil with each other and on solving we get minus 20m is equal to 0. This implies 20m is equal to 0. This implies taking m common m into 20m implies either plus 20 is equal to 0. This implies m is equal to 0 or m is equal to minus 20 by 21. As equation number 1 now putting equal to 0 in equation number 1 we get y is equal to 0 into x plus this implies y is equal to 5. Now putting 2 by 21 in equation number 1 we get y is equal to minus 20 by 21 into x plus 5 into root 1 plus 21. This implies 20 by 21 into x plus 5 into root 1 plus 400 by 441. This implies y is equal to minus 20 by 21 into x plus 5 into root on solving this we will get 841 over 441. This implies y is equal to minus 20 by 21 into x plus 5 into 29 by 21 with 21 it will be 21y is equal to minus 20x plus 145 plus 20x minus 145 is equal to 0. This was the solution of the given question and that's all for this session. Hope you all have enjoyed this session.